This page is about speaker
matching transformers.Fig 1 to 13 show details of
transformers and all is explained.

There is
sometimes a good reason to use a transformer between an
amplifier and speaker to improve the sound quality
and improve all measured parameters in terms of power ceiling
range, distortion, bandwidth, and
damping factor.. The transformer is called a
Speaker Matching Transformer, or SMT, and is usually a black box connected by short cables from
amplifier and to which existing speaker cables may be plugged
in.

In most cases, the transformer
effectively converts a low impedance speaker to a higher
impedance.

Definitions
of terms used here :- R is resistance in ohms, and R
= V / I where V is voltage in volts applied across R, and I is
amps of current flowing through R as
a result of applied V. RL is Resistance Load, which is
the resistance of a wire or manufactured resistor used in a
circuit where active devices such as
vacuum tubes or solid state cause a change of current to to
liberate power. RLdc = load between a DC supply
rail and a device to change current, RLa = load for ac power at an
anode, RLa-a = load for two push-pull
anodes of two tubes supplying opposite phased voltages to RLa-a. P is the symbol of power is in
the form of heat measured in Watts and may be calculated P = V x
I, or V squared / R or I squared /
R. Po = power output, Pin = power
input. L = inductance in Henrys,
millihenrys, mH, or millionths of a Henry, uH. Lp = primary inductance of a
primary winding, Lsec = secondary winding inductance. LL = leakage inductance between
two windings. C = capacitance in Farads, F,
millionths of Farads, uF, or billionths of Farads, nF, or 1,000 billionths of a Farad,
a pico Farad, pF. X is Reactance in ohms for
either L or C. The ohm value is only valid for only one
particular sine wave frequency. Reactance value of C = XC, and
of L = XL. XC = 1,000,000 / ( 2 x pye x
Frequency in Hertz x C in uF ) = 159,000 / ( F x CuF ) ohms. Hertz = frequency measured in
cycles per second, Hz, or kilocycles per second, kHz, or
millions of cycles per second, MHz.. XL = 2 x pye x F in Hertz x L
in Henrys = 6.28 x F x L ohms. Ra = dynamic anode resistance
on ohms. µ = amplification factor
of a vacuum tube. µ = also means iron core
permeability, a number that varies with F and applied Vac so
context of µ must be remembered. gm = device transconductance in
A/V or mA/V. Z = impedance, nominated in
ohms, and for any combination of R, L or C connected together, and such parts of circuits with
R plus L and/or C are called networks. The impedance of any network measured between any
two points is dependent on frequency of the sine wave voltage applied from one point to
another. The calculation of impedance between two points
connected to more than one R and L and C can be almost
impossible to work out, and is best worked by use of applied software and PC,
although simple R+C and L+R networks can be easily calculated.
But without computing, an approximate estimation of Z may be
made and values trimmed by measurement
until wanted F response and Z is obtained. The following formulas don't
include frequency F. But ohm values of XC or XL do include frequency.
I make no apologies for saying you have to consider many things
if you are to make
accurate calculations
about L&C&R networks, and you must be careful when
measuring them. Its no use chucking a tantrum
when I expect you to
understand details and to calculate and consider things that are
not simple!!!!!. For example, For R + C in
parallel, Z (R//C) of network = 1 / square root of ( 1/R squared
+ 1/XC squared ), Z in ohms, R in ohms, C in
Farads. For R+C in series, Z ( R+C) =
square root of ( XC squared + R squared ) in ohms where R is
ohms, C in Farads and XC in ohms. Similarly, for R + L in
parallel, Z (R//L) = 1 / square root of ( 1 / R squared + 1 / XL
squared ) ohms. For R+L in series, Z(R+L)
= square root of ( R squared + XL squared ).

Eg, XC for 2uF is 79.5 ohms at
1kHz. Impedance of say R = 79.5 ohms plus 2uF in parallel is 56.2 ohms. Where XC = R then
XR//C = 0.707 x R. In series, 79.5 ohms plus 2uF
has Z = 112.4 ohms. Notice the XC+R = R x 1.414. You will have to study many
more examples plus a mountain of theory and equations for which
I don't have time or space to
include here. Many keen audiophiles are utterly dumb and unable
to consider the world in terms of
applied mathematics, and its why their own attempts and
designing gear are so ineptly incompetent
and bad sounding, and likely to generate smoke.

A typical speaker may have an impedance of
4 ohms printed impedance on the label. But the construction of the
speakers include drivers which have complex R+L components and
some C if the box effect is
added. A simple 2 way crossover network board may have 15 L, C
and R parts included, and the final actual
Z cannot be easily calculated by anyone on the Planet. But the Z
will be a finite value at each
frequency considered and the"average" Z between input terminals
is the "nominal impedance". But Z may
in fact vary between 2 ohms and 30 ohms depending on any single
frequency applied. There may be
a region of say between 100Hz and 500Hz where Z = 4 ohms, +/- 1 ohms, so the speaker is
called a "4 ohm speaker" There are speakers which have Z which
may be "difficult to drive" and these
may have their lowest Z in the band of frequencies where most
audio music energy occurs between 100Hz and
1kHz. Old AR9 had two awful quality 3.6 ohm x 11" bass drivers in parallel and with the
crossover the Z input was just above 1 ohm at 120Hz. This caused
many amplifiers to fail from
overheating. But AR9 sold for $4,500 in 1975 and ppl bought them
because manufacturers know how to
market garbage product, and buyers are so damn gullible.

There are reasons why it is not wise to connect
a speaker with any low Z down to say 2 ohms to any amp that has been
designed to work with 8 ohms. If you wish to damage your
amplifier, this is what you do, and it
defies common sense. Common sense says less ohms are easier to
drive. Like less bricks on the truck
mean the truck can drive up the hill easier. No matter what I
say, ppl don't remember MORE Ohms =
easier for amp, LESS ohms = harder for amp.

The lower the speaker ohms, the
higher the current needed to produce the same power output and sound level. If a speaker
sensitivity is rated for SPL = 88dB/W at 1M, then for a "4 ohm"
speaker the amp voltage is 2Vrms and
amp current is 0.5Arms. ( This assumes the Z is constant for all
F and that the sensitivity is constant,
but both vary considerably, so manufacturers just give the
nominal or average value.) For 10 Watts into 4 ohms you
need 6.3Vrms and 1.58Arms. There may be a dip in Z to 2 ohms at say 200Hz and where
sensitivity is much less. The same amp voltage of 6.3Vrms
generates 3.15Arms. The speaker may have a high
reactive L or C component in its "load nature" which is the sum of L, C and R elements in
drivers and crossover filters all acting together. Some amps
would not perform well with 2 ohms and
high currents even though they have a high maximum power output
rating.

This previous paragraph has
bamboozled everyone reading it, so its time to look at diagrams which may break through the
"clouds of dumbness" which affect your brain every time someone rattles off a pile of figures
in text.

Fig 1. The above shows a typical set
up where someone may wish to ensure that a speaker with a
nominal Z that is either above or below
the ideal load value for the amp can be converted into an
impedance that is ideal for the
amplifier, and hopefully the resulting music replay will include
less amplifier distortion, will not cause tubes to
overheat, and will give better damping factor, and all of this
without winding losses exceeding 5%, and without
reducing the bandwidth of signal applied to the speaker.

Let us suppose we have a fairly
well made tube amp such as one channel of my 5050 at
http://www.turneraudio.com.au/Integrated5050.htm

For this amp, 8 ohms is a very
nice load for each channel. In fact, all speaker loads between 4
and 16 ohms are very well tolerated,
and one would not really need a SMT at all. Suppose the 5050 had only one
one pair of output terminals labelled "8 ohms". Suppose I wanted to power a two
ohm speaker, or 2 x 4 ohm speakers in parallel. Then the SMT would be a good
idea, because 2 ohms is a dangerous and bad sounding load to
connect, especially if it has low
sensitivity needing high power to generate a wanted sound level.

Many people will purchase the
most powerful amplifier they can afford, and then buy the most
expensive speakers without worrying about
sensitivity, impedance, load matching, or power, or anything
else at all, except how to get it home and
hook it all up. What a dumb and uneducated approach!

Well, 95% of the world's people
cannot be expected to be fully educated on how things work. So they have to use guesswork
or salesman's advice and/or user manuals and perhaps online
information to set up their system. Advice
is all minimized if they buy a complete 3 in 1 box of
electronics and speakers as a matching package. 5% of
music listeners expect more hi-fi than is available from bargain
basement mass produced "packages" costing
under $500. Some are extremely fussy about sensitivity,
impedance, load matching, and power
because they know that if they understand these issues and apply
the knowledge they don't have to spend so
much as those who buy far more expensive amps and speakers.

Fig 2. Here is a nice tricky little
picky if ever there was one!!

Before 1955, it was established
by authors of the 1955 Radiotron Designer's Handbook, 4th Ed, on page 623, that maximum sound
levels for men and women was 78dB for symphonic music. Maximum levels for musicians
was 88dB, and highest levels for male "programme engineers" was 90dB. Today, any tests may
show men and women may prefer slightly higher levels especially
since higher levels of bass
exist in much pop music and film sound tracks et all. Older
people like lower SPL than younger
people, unless they have gone deaf. My tests using simple SPL
meters in lounge-rooms reveals that 85dB is a maximum average
for most people, for most music.
Classical orchestral music may linger at average levels much
lower than 85dB, but also soar
briefly to 100dB. Much pop music will sit between 85dB and 91dB,
with very little change to level
because of compression and repetitive drum and bass levels and
because of young people's preferences
for continual Boom-Chikka-Boom & rap garbage.

For most serious hi-fi
listeners, their speakers and amp must be able to make SPL =
100dB at least. Their average level may be say
85dB.

So let us suppose you buy a
pair of speakers, say X-Brand, rated for 88dB/W/M, ie, the
speakers produce SPL = 88dB with say
1kHz sine wave at distance of 1 metre with 1.0 watts applied, and all done in an anechoic
chamber. Inside a nicely carpeted room with lounge chairs and
some absorbent furnishings to reduce
unpleasant reverberations, the 1.0 Watts applied may produce
88dB SPL at 3 metres, allowing for reflected sound.
Music energy is a mix of very many frequencies in dynamically
varying levels and one should find the
quantities mentioned so far will be about correct. Hi-fi systems
will have two speakers for stereo so that to
make an SPL of 88 dB, only 0.5 Watts need be applied to each of
two speakers to make an SPL of 85dB
in each. Each change of +/-3dB of SPL measured requires a power
change of +/- 6dB of power, in
other words, to increase SPL +3dB, twice the power is applied, and to reduce the SPL -3dB
means 1/2 the power is needed.

Now because average room SPL
may not be more than 85dB, we need only have each speaker produce 82dB, and if we look at
the table 1 in Fig 2 we see only 0.25 Watts is needed for each
speaker and together, 2 speakers
produce 85d.

Table 2 in Fig confirms the
power needed for average 85dB and only 8 Watts per channel is
needed for total room SPL of 100dB. If
each amp can make 24 Watts, then max SPL will reach 106dB which
usually is plenty for most ppl. Most
recorded music has had its dynamic range limited or compressed
and the 85dB to 106dB is enough,
although in the real world without electronics some acoustic
instruments may produce SPLs much higher where
microphones are placed near instruments, and sitting in among
the brass section of a large orchestra
requires ear protection.

Therefore, the use of 2 x
6550/KT88/KT90/KT120 in each amp channel usually gives "enough"
power.

But whether it really is enough
can depend on impedances, not just sensitivity. The more
sensitive the speakers, the less power you need. Most
are now made at about 88dB/W/M and many are 4 ohms, with dips to
2.5 ohms. Fig 3. The two graphs show what power
may be expected from 2 x 6550 ( or KT88 etc ). The graphs are prepared from
tests carried out on an amp with given operating conditions and with OPT
matching giving 8k0 : 8r load matching setting.

The PP amp can give up to 55 Watts with a 3
ohm load, but that doesn't mean you must use a 3 ohm load. With loads less
than 4 ohms, THD becomes high because class A working portion is a low % of total possible
class AB power. And the amount of effectively applied NFB is
low. Damping factor is worse. With 8 ohms, you get 35 Watts,
and perceived SPL maximum at clipping is only -2dB and almost a negligible amount compared to
having 55 Watts. 35W of class A power, low THD, and good DF will sound better. The variations with THD when
using different loads can be seen in THD graph in Fig 2. The THD levels have been drawn
on a logarithmic scale, so you need to read the variations
carefully. Basically, the higher the
speaker ohms, the lower the THD and lower all other distortions
as well. But if load is say 16 ohms,
then available max PO is only 18 Watts. But it is all pure class
A PO and with low THD, so if clipping
does not occur, music may sound best with the 16 ohm speakers - if the speakers don't create
distortions. My PP amps have maximum PO
possible with a load of less than 1/2 the nominal speaker Z, ie,
max PO occurs with 3 ohms,
although terminals are labelled "8 ohms". Many amps make the
maximum PO of say 55 Watts occur with
the labelled 8 ohm load, ie, their OPT would have a Z ratio of
3k0 : 8 ohms, not 8k0 : 8. This means that the amp with
3k0 : 8r OPT surely would not work well if a 4 ohm speaker with
dip to 2 ohms was connected. The tube
load then drops to1k5, with dip to 1k0. The THD/IMD with a "4
ohm load" would be many times greater
than with 8 ohms or to anything I would make.

Many mass made amps may have
output terminals labelled 4 ohms and 8 ohms, but what works best
is 8 ohms and 16 ohms
respectively. To overcome such a problem, the SMT with 2:1 turn
ratio can make a 4 ohm speaker look like 16
ohms. Then the tubes work with a higher RLa-a ohm load value
which gives lower THD/IMD and better
DF and bandwidth etc.

The SE amp with 2 parallel 6550 has a
very different OPT, and the tubes always work in class A. Load matching is more critical
than for any PP amp of the same Po, because SE amps cannot
generate class AB Po that can be up to 3
times the maximum pure class A Po maximum In the SE amp case, maximum
class A power = 22 Watts is made when load is 8 ohms, and loads
of more or less ohms will always
give less power. If a speaker was 4 ohms with a dip to 2.0r then
you may expect a poor sound at high
levels because only 12 Watts is available, and any signal F
where Z = 2.0r gives only 8 Watts. The
impedance dip in speaker Z character will cause terrible IMD and
THD at all but very low levels.The max
power with 16r will also be less at 13Watts but at least this
power will have low distortion and DF will be
high.

Consider old Quad-II amps. These have a pair of KT66
with OPT arranged to give a Z ratio of 4k0 : 9 ohms or 16 ohms. But
many ppl try to use 4 ohm speakers connected to the OPT when terminals under the chassis
have been strapped to suit 8 ohms. The RLa-a on tubes becomes
only 2k0, and this is far too low for
fidelity. But best lowest winding loss connection is the "16
ohm" setting of the OPT strappings. The best load
is 32 ohms that gives 18Watts, all class A with RLa-a tube load
of 8k0. Using a 4 ohm speaker with
SMT which has a ratio of 32r : 4r, ie, ZR 8 : 1, TR = 2.83 : 1 means the 4r speaker looks like
32r at the amp and sound will be excellent, ( providing all
other old things in the old Quad amps
have been serviced or replaced.

OTL amps. An OTL amp is said to be usable
with a "4 ohm" speaker. My experience tells me just
about all OTL amps work better with a much higher load value,
maybe 16 or 32 ohms. There are OTL amps where the
use of a 16 ohm speaker will increase available maximum output
power, increase damping factor by 4,
and reduce THD/IMD by 1/4. Let us examine why raising the RL
ohms improves the sound, and all measured
functions. Fig 4. The Fig 4 shows the Ra curves
and class A and B load lines for one 6AS7 with both its triodes
paralleled. As you can see,
loadline A-Q1-B shows near linear intersection of Ra curves
gives 7 Watts of pure class A1 with
RL = 630 ohms and with total Pda at idle = 18 Watts. Using two tubes in PP and class
A1 would give 14Watts and 2H is cancelled leaving a probable 1% 3H with RLa-a = 1,260 ohms.

The class B1 operation shows
RLa = 32r with peak Ia = 740mA, and Ea swing = 22Vpk. I would never risk class using
class B2 by forcing grids positive. In the example, pure class B
with zero Iadc at idle is not used; there
is some low idle Iadc at idle, but Pda calculations then become
the same as for pure class B. 2 x 6AS7 could manage 7Watts in
class B1 with RLa-a = 128 ohms using a normal PP OPT. With a Circlotron, primary OPT
load becomes 32 ohms, and with 8 tubes primary load = 8 ohms and there seems to be no need
of an OPT, ( but of course there is, afaiac ). Pda a rises to 24W max for each
tube in such an amp. It could be higher depending on the idle
Iadc. Tube current production is not
very linear, and the low power region of a few Watts has high
THD%. Tubes work in a region of
borderline safe working. The use of a 4 ohm load could push peak
Ia max in class B1 to about 0.9Amps
with each tube having a load of 16 ohms. Pda could be at least
28W in each tube. PO for 8 tubes
loaded with 4 ohms is 24Watts max and less than PO for 8 ohms. Distortion damping factor is
very poor for all loads without any OPT.

Most OTL need to have 40dB of
GNFB applied to force the circuit to measure acceptably. This is possible because there
is no OPT with its inherent phase shift at LF and HF which is
included in the FB loop. An SMT does not
need to be included in any NFB loop. The SMT can reduce the amount of GNFB needed to 12dB,
and at least one gain stage may be omitted. Output power maximum
can be doubled, with mach more
class A1 Po.

I can conclude that class B1
with 6AS7 is the worst way to use tubes, especially with a very
low value of RL. an SMT will allow better
operation for an amp set up for B1 and can have increased idle
tube current for class AB1 and a
much higher % of class A power.

High power tube amps or SS amps
may be more load tolerant because people use the same power for the same sound level
regardless of the power amp capability.

Nearly all high power tube amps
capable of say 70 Watts+ will be found to produce say 0.4
% THD at the 70Watt level or just
before the wave form begins to develop visible flats on the
crests of sine waves which is usually about 2% THD.
So if speaker is 8 ohms, then amp Vo = 23.6Vrms. But average listening levels may be at
0.5Watt which is 2.0Vrms, and THD is approximately proportional
to Vo, so THD at 0.5W = 0.4% x ( 2
/ 23.6 ) = 0.034%, and by calculation THD is quite negligible. If a 2 ohm speaker is used, and
volume is adjusted to make the same power of 0.5W, then Vo =
1.0Vrms. What would THD be then? One may
find max 2 ohm power = 35Watts, at say 1.0% at Vo = 8.3Vrms, so at 1.0Vrms, expect THD = 1%
x ( 1 / 8.3 ) = 0.12%.

THD has quadrupled because load
value has been quartered - for the same sound level.

If the amp has maximum 22Watt
capability for 8 ohms with 2 x 6550 in PSE, expect Vo =
13.2Vrms, with THD = 1%, a higher amount
than for a PP amp because all SE amps tend to make much more THD because there is no
cancellation on even H from push-pull operation. Expect the 0.5Watt THD level to
be 0.15%, more than 4 times the 70Watt capable PP amp. If speaker is 2 ohms, max PO =
6Watts at 3.5Vrms and 1.5% THD. At 0.5Watts with 2 ohms, THD =
0.43%.

Again we see a huge THD
increase just because 2 ohms is used instead of the correct
design load of 8 ohms.

And we also need to say the
lower the maximum power is for the amp, the higher the
distortion becomes for the same listening
levels.

To avoid the THD and resulting
IMD increase, the use of SMT is well justified!

When the amplifier power is
close to the minimum we think we ever would need, we might then remember these
considerations :-

1. We should always try to
provide the amp with a speaker load ohm value it prefers.

2. The speaker ohms between
50Hz and 1kHz should always be higher than what is labelled on
the amp terminals.

3. Use of SMT to reduce amp Vo
but increase Io between amp and speaker will give the amp the higher load ohms it prefers.

4. Impedance matches available
with SMT should be approximately as in the table :-

TABLE 1.

Primary
Input load ohms

Sec = 0.5 x
Pri load

Sec = 0.25
x Pri

Sec = 0.125
x Pri

Sec =
0.0625 x Pri

64 Ohms

32 Ohms

16 Ohms

8 Ohms

4 Ohms

32.0

16.0

8.0

4.0

2.0

16.0

8.0

4.0

2.0

1.0

8.0

4.0

2.0

1.0

0.5

The power handling ability of
the SMT must allow at least 50 Watts with any load value and
winding resistance losses to not be
less than 5%. The cost of manufacturing SMT with a 50Watt rating
will be little different to a 25Watt
rating.

For 50 Watts of input power for
64 ohms, primary input voltage will be higher than for any other
load value and be 56.6 Vrms. The core
saturation at 56.6Vrms should not occur above 14Hz. This
requirement for voltage capability is
independent of current ability. This means the maximum permitted
Bac < 1.6Tesla at 14Hz.

The number of turns in the auto
transformer winding is determined by the formulas elsewhere at
this website for PP OPT design. But the following formula from
the OPT design pages applies :-

Many DIYers may find they
have a pile of old transformers from which they think they might
make something useful, such as a
SMT. Usually, the most common old
E&I lamination size useful for this application will be
"wasteless pattern" with tongue = 38mm and window
size of 19mm x 57mm. The iron quality of most old transformers
is mostly quite poor. This is
because the core has low maximum permeability, µ, often
below 2,000, and has high hysteresis losses
and generates high THD at F below 100Hz. And this is because the iron
may have a low silicon % content and it has not been cold rolled
and annealed to align metal
crystals, ie, worked and heat treated. So I can't really
recommend that you try to use the iron from
old mains transformers with poor quality iron.

For the best SMT or for any OPT
handling audio F signals, you need GOSS laminations, and GOSS means "grain oriented silicon
steel" and this is much harder to ever find among old piles of
fused transformers which nobody
wants.

So, for SMT, you need to BUY
core material, and that upsets hobbyists who hate paying for
anything. You need to know what weight
you need, perhaps 10Kg, and if price is $25 per Kg, there's
$250, and does not include freight.
Finding a supplier willing to supply less than 50Kg of core
material is difficult, and you must expect to pay far
more per Kg than if you were to buy 1,000Kg, an amount that may
be a minimum quantity from large
makers of laminations.

The issue of transformer
generated distortion cannot be treated lightly. Iron in all
audio transformer cores can generate distortion
harmonics greater than the vacuum tubes where the amplifier
output resistance is high. In the 100Watt SMT
described in detail below, the iron distortion even with GOSS
may over 10% at typical levels of listening
where the signal source resistance is over 100 ohms. The
distortion is a mainly odd H harmonics, 3H,
5H etc. The 100W SMT below has primary Lp = 4H at 50Hz so the XL = 1,256 ohms. Let us say the
signal source R = 600r. One may find THD = 12%. The current flow in the winding
without any load with 5Vrms applied and 50Hz is only 4mArms, and
distortion current at 12% is
0.048mA, a very small current. One can say that the the primary
winding has the properties of a linear
perfect primary inductance where 4mArms flows, and also has
a network of equivalent non linear
circuit elements which produce 0.048mA of distortion
currents.One may say the non linear network causing
distortion has a high impedance averaging V / I = 5V / 0.048mA = 104kohms, a quite high
impedance. The SMT is designed to be used with an existing
amplifier with Rout of less than 1 ohm, and when
this is done the distortion current and its impedance still
exists, but the distortion voltage is shunted
by 1 ohm, and its hard to measure the iron caused distortion as
a result. With low grade iron with lower
Si content and less cold rolling to align crystals, iron caused
THD may be 50 times worse than
figures I have mentioned for GOSS here. So hence low grade iron will show some distortion with
the low signal source resistance. One will find that where iron
cored items are used with vacuum tubes, OPTs, and choke
loadings, pentodes are not used without
NFB because because their Ra is a high Z current source and THD
will be atrocious. It is also
bad practice to use the drain circuit of a mosfet to drive a
transformer unless there is a good amount of loop
NFB.

The inductive reactance of a
winding with turns around an iron core show that the primary
inductance Lp is low at low levels of amp
Vo, and then Lp becomes higher as the sine wave amplitude
increases, and then Lp becomes lower when
the core material reaches onset of saturation. This is the
nature of non linear iron behaviour.
High enough Vac across the winding results in a cessation of
change in magnetic field beyond say
1.6Tesla. When this occurs, magnetic field is static, and cannot
cause the opposition of current
flow and reactance reduces to zero, and core has become "magnetically saturated". This
can occur for part of a sine wave for where Bac is forced above
1.6Tesla, but magnetic field
cannot increase. Thus for the section of sine wave where applied
voltage would cause Bac to exceed 1.6T,
the actual impedance becomes no more than the wire resistance. Saturation is proportional to
frequency, so the lower the F, the higher the Bac and the easier
it is to have saturation. LF caused
saturation can cause a sudden enormous rise in THD and IMD and complete lack of fidelity with
music. SMTs should allow full 100 Watts into the primary load of
say 8ohms and at just above the
Fsat which should be close to 10Hz. It is saturation behaviour
that determines the turns and Afe needed for a
primary winding's "turns per volt", and not the calculated
primary inductance.

To minimize the distortion
caused by iron which is always worst at F below 100Hz, GOSS
should be used, and to reduce sudden
onset of core saturation the core µ should be reduced from
the high values found with GOSS, perhaps 15,000
with some E&I samples, to no less than 3,000. This makes the
iron behave as an inductance with
less sudden saturation at LF, and is better than having a high
inductance that becomes a short circuit if
the core is saturated if stray LF below 20Hz are applied at high
voltage amplitudes. The amplifier driving a SMT
must have low output resistance, preferably less than 1/10 of
the load value to be driven, easy to obtain
from most amps where NFB is applied within the amp. But some OTL amps have quite
high Rout and quite a poor damping factor. However, if you
connected a SMT with 64 ohms input load
to drive a 4 ohm speaker, then Rout of the amp need only be as
low as 6.4 ohms to get a DF = 10.
Iron caused harmonics will be suppressed by whatever FB is
operative, including that which exists in
the triodes without the NFB loop added. Using solid state
devices such as mosfets in source follower mode
and with global NFB can mean Rout < 0.1 ohm, and iron caused
distortion is easily reduced to
utterly negligible levels, and the iron ceases to "get in the
way of the music".

THERE ARE EXAMPLES of other
speaker matching trannies which use an auto transformer with ONE
winding to give input as 8 ohms
and with with taps offering use of speakers with Z = 4, 2, 1,
0.5 ohms. A classic modern example is
made by Paul Speltz at http://www.zeroimpedance.com I have tested one of Paul's
toroidal transformers. I found it had excellent bandwidth. Two
audiophiles here in Canberra bought them and were
well pleased. One bought the simple un-boxed version which I was
asked to enclose in a box. I
made a wooden box and mounted the tranny inside and surrounded
with compacted dry sand. The lid had
foam between lid underside and sand surface to keep some active
pressure on the contents. Transformer was
siliconed to bottom of box so movement creep is not possible.

I found toroidal windings were
very messily wound but the measurements were very good. It may
be difficult for any DIYer to duplicate this
performance of wide bandwidth unless he knew the secrets of the
sequence of layers of windings and their
relative position around the toroid circle. Inherently, toroidal
transformers offer broad bandwidth because a
primary and secondary windings are well interleaved if each are
wound around the toroid in several
layers which overlap all the way around.

THE DIY SMT BUILDER will
probably find it easier to use E&I laminations or C-cores
and use a preformed plastic winding
bobbin.

Any single winding transformer
with taps, ie, auto-transformer that you may be tempted to wind
at home may suffer much reduced HF response
at secondary taps especially if secondary load is lower than 1/2
the input load. Despite auto transformers
having only one winding, as the the portion of shared winding
used for a secondary winding becomes smaller, the
transformer behaves like an isolation transformer which has a
low number of primary and secondary interleaved
sections. Consider you have 8 layers of wire on a given bobbin
for one winding, occupying a window size of 19mm x 57mm.
Say you devote the bottom two layers for a secondary for 2 ohms.
The TR will be 8L to 2L, or 4:1, so
primary load input = 8 ohms. You may find than HF bandwidth does
not reach 8kHz. To increase the bandwidth, the
2 layers used for 2 ohms should be from 3rd up and 6th up from
bottom. the series connection is the same, with 6
layers from top to 2 ohm tap, and then two layers to 0V. But
then you will find winding losses will be high and
BW still rather low, so then you need to increase total layers
and have maybe 2 extra layers in parallel with
the 2 layers for 2 ohms. Then the core window needs to be
increased, or stack height increased to reduce Np, and
then the design exercize will take a week, not just one evening
with pocket calculator using print-outs of my design
pages on your kitchen table.

There are some toroidal mains
transformers which have 2 x 115Vac primary windings with say 2 x
50Vac secondary windings and rated for 300VA.
These are used for PT in solid state amps where +/- 70Vdc is
wanted. There are those who may be tempted to use these
as SMT. But the range of available load matches is very low, and
many problems will remain and I cannot
recommend the use of any mains transformers for audio hi-fi
applications.

To test a SMT, I found it
necessary to use an amp with Rout less than 2 ohms and bandwidth
of 2Hz to 3MHz. Most amplifiers cannot produce
the necessary bandwidth, 10Hz to 65kHz is common. But for
TESTING audio transformers one always
should explore behaviour beyond ordinary bandwidth.

Test signal levels do not have
to exceed 3Vrms for SMT. This means that an elaborate multi
stage amplifier need not be used for a test signal.
All that is needed is a mosfet based buffer amp with no voltage
gain and which merely lowers the source resistance of
the test signal voltage from a standard 600 ohms to less than 2
ohms. Here is what I have used :-

Fig 5. The buffer stage allows
adequate testing of any audio transformer at F above core
saturation, say 10Hz to over 4MHz when secondary is
loaded with specified RL, or not loaded at all with R, or loaded
by any R+C network or with a pure C
load. Test loading with L may also be done with caution at low
F.

However, when using such a
buffer, LF core saturation performance may be difficult to test
with signals taken to the primary input where signals
across windings is the highest . The 100W SMT below is rated for
100Watts into 8 ohms which means 28Vrms may
be applied across the primary and at 10Hz when calculated Bac =
1.5Tesla. At this condition the core
should produce distortion exceeding 3% and easily seen on the
oscilloscope. Therefore one would need an
un-distorted input signal to the buffer stage of about 30Vrms
and going down to 2Hz. The buffer shown here
cannot produce more than 10Vrms, so core saturation may not be
able to be tested using the primary
winding. However, it is possible to use a secondary winding
which has far fewer turns than primary. For testing
to confirm Fsat, the transformer may be tested without any R
loading at all across any winding. But the
there should be a small 1r0 current sensing resistance connected
between earthy end of a secondary or a
portion of primary and 0V. The voltage across the 1r0 is then
fed to an oscilloscope, and when
saturation begins to occur, there will be a very rapid rise in
THD as F is lowered.

Suppose you have calculated
that Fsat = 10Hz at 28Vrms across the primary winding. Suppose you have a secondary
winding has 1/4 of the turns of the primary. You should find
that Fsat = 10Hz when 7Vrms is applied
across the secondary winding. The only worry is about the
secondary winding inductance, and that
its reactance not be too low at such low F. In the case of the 100W SMT,
primary Lp = 4H, and with a sec = 1/4 of the turns the sec L will be 4H x 1 / (4 x 4) =
0.25H. The reactance of 0.25H at 10Hz = 15.7 ohms and this will
not cause excessive amplifier
currents and overheating. But when saturation does begin to
occur for parts of the sine wave
applied, there will be very high current produced which may well
cause mosfet overheating if
sustained for longer than a few seconds. So the measurement of Fsat must be done very
carefully.

There are TWO basic options for
SMT, either Isolation transformer OR Auto-transformer.

My experience tells me its
easier to design the isolation type for best predictable fair HF
response than design the auto-transformer, but both will
be discussed here.

Let me deal with basic issues
with an auto-transformer....... Fig 6. This shows a very basic set of
amplifier powering a speaker with an SMT connected. The advantages of
auto-transformer are that winding resistance losses are lower
than isolation transformers for where the secondary load is not
less than 1/2 the primary load. Consider the winding currents in
the above auto transformer. In the
non-shared portion of A to E and F to B the primary input
current = 1.75A for the 120 turns, and if the Rw = 0.5
ohms, the power lost = 1.53Watts. But the current in the
remaining E to F secondary winding which powers the speaker will
be found to be the difference between speaker
current and primary current = 5.25 - 1.75 = 3.5A. The turns for E-F = 60t, and if
the same dia wire exists for all windings, Rw = 0.25 ohms and
losses = 3.06 Watts. Therefore total P&S losses
would be 4.6 Watts, ie 9.2% of 50Watts applied to input. The
above diagram showsPo at sec = 49 Watts, which is
extremely optimistic and in fact one would get about Po =
45.4Watts.

If an isolation transformer
were to have a primary winding of 180t using the same wire wire
size then more bobbin window area must be found for
the 60t for isolated secondary, so the window size must be
larger. This involves a larger core size, but with
lower stack height to keep Afe the same. But weight has
increased. And turn length may increase. The 180t for
primary carries 1.75A and Rw may become 0.9r so losses =
2.75Watts. With 60t for secondary using
same wire size, Rw = 0.3r and current is the same as for speaker
at 5.25A so sec winding losses =
8.27Watts, so total P+S losses = 11.0 Watts. Total losses are
22%.Po at sec = 39 Watts.

To reduce losses for BOTH types
of transformers requires slightly different methods. For the auto transformer, the
winding E to F would in fact comprise two paralleled windings
each 60t. This would halve sec losses to
1.53 Watts, and total P+S loss = 3.06 Watts, or 5.7% of 50Watts
of input power.This means that there would be 8
layers of wire with two of them paralleled with another two for
between E and Fand these 4 windings would then
be spread out among the remaining 4 to minimize leakage
inductance to getbest bandwidth.

The isolation transformer would
need to have a much bigger window, AND to get lower resistance
losses the wire size must also be increased
AND to reduce the number of turns for same Fsat the stack height
must increase.The secondary would need to have
paralleled windings and/orlarger wire size than the primary. I cannot give all details but
you will find the conventional isolation transformer will need
to be twice the weight of the auto transformer to
achieve the same power handling, Fsat, and winding losses, and
an example of isolationtransformer is below......

Fig 7. In order to get reasonably low
winding losses with the isolation SMT, the core size must have a
larger window size to accommodate
larger winding wire. Should anyone wish to have the
primary used with a Vdc potential of say up to 100Vdc, they can
do so safely without worrying about
the secondary and speaker also being at a Vdc potential. But I draw the above with both
P and S windings taken to 0V at one end. The method of changing the load
matching is done by changing secondary connections with soldered
wire links or bolted metal
strappings. I suggest this is rather inconvenient for 99% of
audiophiles.

There are 12 primary connections
numbered 1 to 12 in winding order and all connected in series.There are 12 secondary
connections, A to L. I have not included details of how you
would arrange a circuit board allow an easy
change of P to S turn ratios, but one way is to have an octal
tube socket on the SMT board for banana
sockets for amp and speaker cables. The strapping pattern may be
varied using octal plugs with prepared linking patterns within
the 8 pins. Suppose you wanted to
make most available speakers between 3 and 9 ohms appear as about 16 ohms to an amp. One octal plug would be strapped
for 72 turns to give 16r0 : 2r6, ok for all low Z speakers between 2r0 and 5r0.One octal plug would be strapped
for 108 turns to give 16r0 : 5r8, ok for all speaker Z between5r0 and 10r0. Higher speaker Z can be
connected directly to the amp without SMT.

So probably, only two octal
strapping sockets need to be used, and to avoid losing the
unused plugit should be plugged into a
second octal socket labelled "Spare".

One might be tempted to make the
SMT secondary in the form of say 4 parallel windings each with
taps and just like a tapped secondary on a tube amp OPT. But this means the core window
must be even bigger to accommodate more turns, and by then the
use of a plain old auto SMT with no
isolation between P and S begins to make a whole lot more sense.
So I have not given any more
details, and I leave that to others.

Fig 8. A fairly simple
auto-transformer for 50 Watts :- This is a brief
diagram-schematic of a speaker matching transformer used with an
amplifier to make a range of speaker ohms "look just like" a higher
Z speaker from the amplifier's view point.

Because there are so many
possible load ratios are so numerous, it would be very easy for
someone to use the wrong terminals, or have different
terminals used for each channel. So unless you are able to
confirm what you are doing with well labelled terminals
and / or by means of measuring a test signal of 1 kHz, then just
remember I have mentioned that the marriage of knowledge
and a fool can lead to smoke. However, as long as amp cables
go to A & B, then connection of any speaker to between any
of the terminals C to H will always give a higher ohm
load value between A & B. Many might guess what they are
doing and find they cannot hear what sounds best. And they
just can't understand ohms, voltage, current or impedance, or
why smoke and blow fuses happen so often. I suggest they
confer with a more logical friend.

The input voltage is limited to
40Vrms by core saturation at 12Hz when Bmax = 1.5Tesla. It means
that the SMT could cope with 200Watts of
input to 8 ohms looking into the SMT A & B input. Winding losses are 5.2% when
the input Z is 8 ohms, and speaker load is 2 ohms.

Fig 9. For those confused by so
many connections, here is a board layout and label :-

The highest winding losses are
just over 10% when primary input load is 8 ohms due to whatever
speaker is connected, say 3.55 ohms
connected to the C-H terminals. The input load = 3.55 x 2.25 =
8.0 ohms at A-B.

If the same 3.55 ohms was moved
to the C - G terminals, the load which appears at AB becomes 4 x 3.55 = 14.2 ohms. If the
3.55 ohms is moved to D - G terminals, load at A - B becomes 9 x
3.55 = 32 ohms.

Some people get very nervous
about connection of a speaker load with very low DC
resistance across the output terminals of any amp. Most
audiophiles would be entirely unaware of any danger to the amp
especially if it is a solid state amp. The low winding
resistance of the primary of the SMT is much lower than the
winding resistance of a speaker coil. This is no problem
for a tube amp, but could be for an SS amp which becomes faulty
with a DC offset at its output directly from SS
devices. If DC offset was say 0.5Vdc, and primary resistance of
SMT shown above is 0.5 ohms, then the NFB
circuit of the amp may try to keep the 0.5Vdc constant, so 1Adc
will flow in output devicesin addition to whatever other
idle current may be so that maybe only 1/2 the output devices
are biased with too much current and may overheat while
the other 1/2 have far too little bias current. This causes the
amp to perform as a badly designed single ended
amp for the first watt or two and THD&IMD will be much too
high.

To avoid such problems with SS
amps, a DC blocking cap can be soldered inside the amp between
amp output terminals and output from
devices. A usual value to suit low loads down to 4 ohms without
affecting bass response is 10,000uF, rated for ripple
current of 7 amps. The simplest way to do this is use multiple
parallel non polarized electrolytic caps - if you can
find them. The other way is to use 2 x normal 63V rated 22,000uF
electrolytic caps in series, with +end of
one to amp, and +end of other to speaker terminal. The -ends are
commoned and biased with -50Vdc from an amp
PSU rail. Thus you get C = 11,000uF, and caps are properly
biased with Vdc.LF pole with 8r0 input to SMT =
1.8Hz.The 2 electro caps should each
be bypassed with 2uF and 0.1uF polypropylene or polyester caps
rated for 250V min. Many early solid state amps
used a single PSU rail of say +50Vdc and had seriesed power
transistors wherethe collector/emitter output was
at +25Vdc. There needed to be a large capacitor between SS
devices and speaker connected to 0V. Sugden amps still being made
using the same basic topology of 1969 and use 10,000 uF
electro-caps to couple speakers to the
collector/emitter join which has a bias voltage of 23Vdc
which is 1/2 the single rail of +47Vdc used for these class AB solid
state amps.

Fig 10. Now here is a more
sophisticated SMT for 100 Watts. I have wound this design. Excuse the somewhat messy
appearance. This is a prototype under test.

Fig 11. Transformer core and
Bobbin windings for pictured auto-transformer. The above shows my pictured
100W prototype speaker matching auto-transformer. All details
are shown as clearly as I can arrange for you all and I hope
that nobody becomes completely confused with what is being
attempted here.

The bifilar winding of each
layer is not hard to achieve. One then avoids having wires
leading in across a previous layerof turns to half way across the
bobbin for the ends of the two windings per layer. For bifilar
windings with thick wire, I found it easy to wind on 17
turns across the bobbin with a a gap between all turns. Then a
second winding of 17 turns was wound on slowly
between the gaps between turns of the previous 17 turns. Turns
of both windings were pushed tight together using a
plastic paddle to remove all gaps. That's how 34 turns can be
wound on in two windings, each having the full traverse width
of bobbin.

Fig 12. More details of 100
auto-transformer.. Although it is not obvious in
the above schematic of the transformer, there are in fact two of
the eight layers connected in parallel with two
central layers among the other six layers. This means that low Z speaker
loads are connected to paralleled windings which are
symmetrically distributed in the height of the bobbin windings to give
low leakage inductance and low winding losses. For example, winding 1,2,3,4 is
in parallel with 9,10,11,12, and 29,30,31,32 is similarly in
parallel with 21,22,23,24.

The single winding transformer
has more copper section in its central area to suit low loads,
and to gain symmetrical winding layout either side of
the centre tap. The CT could be
taken to 0V and the two input points driven by a pair of balanced voltage sources, as
indicated here as +/- 14.1Vrms. Such use will very well suit
suit Circlotron topology or simple balanced source
follower with N channel mosfets. Many tube amps have 3 speaker
terminals labelled Com, 4 and 8, and the Com terminal is usually
connected to the 0V rail of the amplifier. The
Com to 8 ohm terminal gives the maximum number of turns of the
amp's OPT secondary winding, and gives the highest
Vout. The Com to 4 ohm terminal from a
tap on the winding gives approx 0.7 x total turns for 8 ohms,
and 0.7 x max Vout.The best use of above SMT is
where the SMT primary from A&B are connected to Com and 8. If a 4 ohm speaker is connected
to G&H, then input load to SMT becomes 16 ohms, which may be
a load for the amp that gives better
performance than if the 4 ohm speaker was connected to Com &
4 amp terminals.Notice that where A&B are
used between Com & 8, and Com is at 0V inside the amp, then
the CT connection on SMT winding MUST be ignored,
and left unconnected to anything.

Fig 13. The above shows the wire link
connections made on the 32 terminals mounted on the transformer
with 16 on each side. Also shown are
the additional wire links to the underside of 4mm banana sockets
for amp and speaker cable banana
plugs. The banana sockets are mounted on a board fixed above the
winding with rows of winding
terminations each side. The board overall L x W is made to suit
the boxenclosing the SMT. A suitable
box made to enclose the E&I laminated transformer can be
made using 1.2mm steel sheet, but with
minimum distance from to any winding or core = 12mm, thus
avoiding any magnetic interaction, while also
providing enough room for dry sand filling, and while giving
magnetic shielding against stray magnetic
field coupling with other transformers etc nearby. Ideally, SMT
should be placed 400mm away from any other
audio components.

Test Results. I tested the above transformer
using the mosfet buffer and 3Vrms sine wave signal source
generators giving 2Hz to 4MHz bandwidth, with Rout
of buffer = 1.3ohms. With no load of any kind
connected, bandwidth for between G&H was dead flat from well
below 10Hz to 1MHz, with a =1dB peak at
900kHz. There was a peak of +3dB at 2MHz and then output
declined at more than 12dB/octave with other
peaks and nulls of lessening levels.Use of a 465kHz square wave
showed some slight ringing frequencies between 4MHz and 10MHz.There were no problem resonances
below 1MHz. Pure C load of 2uF produced no
large amount of ringing, and was better than many other audio
transformers.

With Np = 204 turns for the SMT,
Afe = 44x 50, µ max = 8,000, and ML = 245mm, and at high
signal levels below 50Hz, max Lp =
4Henry at 50Hz. Lp is far larger than we need it to be, and one
may think Np could be far lower than 204
turns, or the µ could be a lot lower. Indeed µ would
need to be MUCH lower if the core were
used for an SE design with say 3 amps Idc present. But this SMT is to be capable
of far more power than possible with SE and having Idc present. Without Idc, the Vac levels are
high enough to need to have high Np to avoid core Bac exceeding
1.5 Tesla above 14Hz at voltage
for rated power power. It is core saturation behaviour which determines quantities of iron
and turns, not Lp.

The core with maximum
interleaving has µ = 17,000. The core E&I lams are
each 0.35mm thick and were bundled in stacks of 7E and
7I and each bundle assembled in opposite directions into bobbin
window. This gave the µ =
9,000, and if the core had bundles of say 15e&15I then
perhaps µ would be between 3,000 and 5,000, thus
further reducing risk of saturation with stray LF signals below
10Hz with high amplitude. Most
audio recordings do not contain such stray LF waves.

The SMT is configured as shown
with a CT winding which suggests the input should be supplied by a balanced pair of
oppositely phased signals from an amp output stage or from
balanced PP tubes or SS devices. But there is no need for the
SMT to have its CT taken to ground where there is just two amp output terminals with one at 0V
and the other being singularly active. The input signal can be
applied with each Input connected to 2
output terminals and speaker signal voltage will be the same as
for a balanced pair of signals with
CT at 0V.

The transformer has numerous
other uses and possible configurations, and may be used for OTL with many 6AS7 or 6C33c
triodes.